Yes, in the past we took this approach in cases where estimates are not hard, ie. we know the tech that we will use, the problem is something that is not new per se, and we are completely aware of potential third party integrations.
If we already have a clear idea of how we could implement your project, we can do it with a fixed scope, budget and a precisely defined time-frame. The process would be similar to what is described in the question/answer above, with the exception of us committing to a hard deadline.
Many of our clients wanted to start this way. Usually, after the first project, they went on to work with us "our way" when we proved that we are truly committed to delivering desired results on time and that we, on a regular basis, exceed what was initially expected of us.
The only cases where we are always taking the “fixed scope” route is when we work with heavily regulated clients (like doing work with the Serbian government).